For each pair of matrices below, find the matrix A+B:
A=\begin{bmatrix} 7 \\ -7 \\ -5 \end{bmatrix} and B=\begin{bmatrix} 8 \\ 2 \\ 4 \end{bmatrix}
A=\begin{bmatrix} -4 & 7 \\ -1 & -5 \end{bmatrix} and B=\begin{bmatrix} 8 & 3 \\ -2 & 9 \end{bmatrix}
A=\begin{bmatrix} -4 & 7 & 3 \\ -6 & 2 & 4 \end{bmatrix} and B=\begin{bmatrix} 7 & 9 & 6 \\ -9 & 8 & -1 \end{bmatrix}
A=\begin{bmatrix} -5 & -9 \\ -4 & -2 \\ -3 & -7 \end{bmatrix} and B=\begin{bmatrix} 1 & 8 \\ 2 & 3 \\ 7 & 5 \end{bmatrix}
A=\begin{bmatrix} 4.94 & -8.56 \\ 2.87 & -8.04 \\ 8.64 & 2.45 \end{bmatrix} and B=\begin{bmatrix} -5.47 & 7.79 \\ -0.54 & 5.73 \\ -2.73 & 4.97 \end{bmatrix}
For each pair of matrices below, find the matrix A-B:
A=\begin{bmatrix} -4 \\ 3 \\ -3 \end{bmatrix} and B=\begin{bmatrix} -2 \\ -6 \\ -1 \end{bmatrix}
A=\begin{bmatrix} -3 & 3 \\ 9 & 2 \end{bmatrix} and B=\begin{bmatrix} -9 & -4 \\ -6 & -2 \end{bmatrix}
A=\begin{bmatrix} 9 & 2 & 6 \\ 5 & -7 & 8 \end{bmatrix} and B=\begin{bmatrix} -3 & -5 & 3 \\ -1 & -6 & 7 \end{bmatrix}
A=\begin{bmatrix} -1 & -2 & -3 \\ 4 & -6 & -9 \\ 8 & 6 & 5 \end{bmatrix} and B=\begin{bmatrix} -8 & 2 & -7 \\ 1 & 3 & 9 \\ 7 & -5 & -4 \end{bmatrix}
A=\begin{bmatrix} 46 & 414 & 215 & 598 \\ 102 & 187 & 363 & 455 \\ 202 & 428 & 589 &341 \end{bmatrix} and B=\begin{bmatrix} 321 & 208 & 106 & 333 \\ 71 & 214 & 228 & 355 \\ 22 & 41 & 523 & 72 \end{bmatrix}
A=\begin{bmatrix} 5 \\ -8 \\ -9 \end{bmatrix}, find 5A.
A=\begin{bmatrix} 6 & 1 & -2 \\ 5 & -6 & 7 \end{bmatrix}, find -4A.
A=\begin{bmatrix} 2 & -6 \\ -4 & 3\end{bmatrix}, find 3A.
A=\begin{bmatrix} 13 & 22 & 20 \\ 18 & 23 & 16 \\ 30 & 24 & 15 \end{bmatrix}, find 6A.
A=\begin{bmatrix} 17 & 28 & 13 & 27 \\ 24 & 23 & 16 & 30 \end{bmatrix}, find 5A.
A=\begin{bmatrix} 44 & 56 \\ 40 & 20 \\ 32 & 60 \\ 68 & 24 \end{bmatrix}, find \dfrac{1}{4}A.
A = \begin{bmatrix} 6 & 3 \\ 2 & 5 \end{bmatrix} and B = \begin{bmatrix} 9 & 4 \\ 0 & 7 \end{bmatrix}, find 4A + B.
A = \begin{bmatrix} 6 & -3 \\ 7 & -4 \end{bmatrix} and B = \begin{bmatrix} 2 & 9 \\ 0 & -1 \end{bmatrix}, find 5A + 3B.
A = \begin{bmatrix} 4 & 0 \\ -9 & 5 \end{bmatrix} and B = \begin{bmatrix} 8 & 3 \\ 1 & 6 \end{bmatrix}, find 3A - 3B.
A = \begin{bmatrix} 1.75 & 0.25 \\ 2 & 1 \end{bmatrix} and B = \begin{bmatrix} 0.5 & 0.75 \\ 1.5 & 1.25 \end{bmatrix}, find 3A + 2B.
A = \begin{bmatrix} 6 & -12 \\ 4 & 14 \end{bmatrix} and B = \begin{bmatrix} 24 & 3 \\ -12 & 0 \end{bmatrix}, find \dfrac {1}{2} A + \dfrac{2} {3}B.
A = \begin{bmatrix} 10 & 4 \\ 3 & -9 \end{bmatrix}, B=\begin{bmatrix} 1 & 6 \\ 7 & -1 \end{bmatrix} and C= \begin{bmatrix} 0 & -2 \\ -5 & 8 \end{bmatrix}, find 4A + 2B - 5C.
If 2\begin{bmatrix} 3 & 0 \\ 5 & 4 \end{bmatrix} - 3A = \begin{bmatrix} 3 & 6 \\ 1 & -4 \end{bmatrix}, find matrix A.
Solve the following matrix equations for n:
Solve the following matrix equations for x:
If \begin{bmatrix} u + 5 & 3v & 8 \\ 8x & 7 & 5 \end{bmatrix} + \begin{bmatrix} 7u & 4v & 2w & \\ 4 & 2 & 25 \end{bmatrix} =\begin{bmatrix} 37 & 49 & 14 \\ 52 & 9 & 6y \end{bmatrix}, find the value of:
u
v
w
x
y
Write down the transpose M^T, of the following matrices:
Determine whether the following statements are true or false:
The transpose of a matrix is made by interchanging its rows and columns.
The transpose of a square matrix always identical to the original matrix.
The transpose of a column matrix will always be a row matrix.
The transpose of an identity matrix is always identical to the original matrix.
The order of the matrix A is 3 \times 4. State the order of the transpose, A^T.
Matrix S is a symmetric matrix. Describe the transpose of matrix S.
The table shows the number of visitors to a website over several months, broken down by country:
| Japan | Egypt | Italy | Thailand | |
|---|---|---|---|---|
| May | 21 | 23 | 59 | 12 |
| June | 37 | 32 | 51 | 18 |
| July | 55 | 27 | 44 | 19 |
| August | 38 | 36 | 42 | 15 |
| September | 54 | 28 | 33 | 13 |
Find the total number of visitors to the site during each month. Express your answer as a column matrix, where the rows list the months in the same order as the table.
Find how many more visitors from Japan than from Thailand there were during each month by subtracting an appropriate pair of column matrices. Express your answer as a column matrix, where the rows list the months in the same order as the table.
The tables show the number of fruit and vegetables sold at Mohamad's three corner shops over a particular weekend:
Saturday
| Fruit | Vegetables | |
|---|---|---|
| Shop 1 | 45 | 55 |
| Shop 2 | 42 | 62 |
| Shop 3 | 68 | 48 |
Sunday
| Fruit | Vegetables | |
|---|---|---|
| Shop 1 | 64 | 41 |
| Shop 2 | 66 | 37 |
| Shop 3 | 36 | 32 |
Write a matrix expression and hence calculate the total number of sales over the entire weekend. Let the rows in each matrix represent each shop and the columns represent each type of produce.
The cost matrix for five products in a health food store is:
C=\begin{bmatrix} 6.90 & 5.40 & 2.90 & 8.70 & 4.60\end{bmatrix}The store adds 150\% to the cost of each product to generate the sales price.
Write a matrix equation to calculate S, the sales price matrix from C.
Write the sales prices as a sales price matrix, S .
Write the profit for each of the five products as a profit matrix, P.
In a particular town, 25\% of households own no pets, 40\% of households own one pet, 20\% of households own two pets and 15\% of households own more than two pets.
Construct a row matrix, P, displaying the percentages in the order given in the instructions.
If there are 900 households in the town, write a matrix equation to find H, a matrix of the number of households in each category, in terms of P.
Hence, determine the row matrix H.
Papa's Pizzeria are about to mark up prices on their items by 50\%. The table shows their current prices:
Construct a matrix M, which contains the marked up prices for the pizza and fries.
| \text{Pizza } (\$) | \text{Fries } (\$) | |
|---|---|---|
| Small | 7 | 4 |
| Medium | 13 | 8 |
| Large | 25 | 12 |
Hallmart will be offering a 10\% discount on all items in their fashion department for their Boxing Day sale. The table shows the prices on Christmas Eve:
Construct a matrix P, which contains the discounted prices for each item.
| \text{Mens } (\$) | \text{Womens } (\$) | |
|---|---|---|
| Jeans | 34 | 25 |
| T-shirts | 38 | 21 |
| Jackets | 28 | 12 |